Determine the type of correlation for the two variables given in the data

[chwala]

Homework Statement

Determine the type of correlation that exists between the two given variables.

Relevant Equations

Pearson's correlation coefficient

Kindly see the attached problem below (i find the topic to be easy and straightforward). My concern is only on the highlighted part:

In my understanding, to define the type of correlation i have always approached a straightforward approach.
For value $1$ perfect positive correlation and value $-1$ perfect negative correlation.
any value between $0.5-1$ strong positive correlation.
any value between $0-0.5$ weak positive correlation.
any value between $-0.5-0$ weak negative correlation and so on...
In addition, i have always considered values $0.5$ and $-0.5$ as either positive/weak.

Is my approach correct?

Now to my question, how did they arrive at the interval on the highlighted part above (in yellow). Kindly see table below as a reference...how did they arrive at the values indicated on the table? or they used some data and then went ahead to see how the data is spread out on the graph (by considering outliers where necessary) ...then used Pearson's correlation coefficient to come up with some deduction...i think that's how they did it.

 

[RPinPA]

It has nothing to do with the specific data. If you have something that goes from 0 - 1 with 0 being weakest and 1 being strongest, you can chop it any way you like and define any names you like to break that up into ranges from "weakest" to "strongest".

You defined categories for |r|: 0 - 0.5 = weak, 0.5 - 1.0 = strong.

They broke it up into finer categories: 0 - 0.1 = none, 0.1 - 0.5 = weak, 0.5 - 0.87 moderate, 0.87-0.95 strong, 0.95 - (less than)1.0 very strong.

0.81 lies between 0.5 and 0.87 so it's in the moderate category.

 

[chwala]

It has nothing to do with the specific data. If you have something that goes from 0 - 1 with 0 being weakest and 1 being strongest, you can chop it any way you like and define any names you like to break that up into ranges from "weakest" to "strongest".

You defined categories for |r|: 0 - 0.5 = weak, 0.5 - 1.0 = strong.

They broke it up into finer categories: 0 - 0.1 = none, 0.1 - 0.5 = weak, 0.5 - 0.87 moderate, 0.87-0.95 strong, 0.95 - (less than)1.0 very strong.

0.81 lies between 0.5 and 0.87 so it's in the moderate category.

you can chop it any way you like and define any names you like to break that up into ranges from "weakest" to "strongest".

thanks mate for this summary.

 

[Delta2]

Thanks @chwala the second picture at the OP is quite nice, made me remember some things about linear correlation, I wasn't particularly good at statistics courses during my undergraduate studies (25-30 years ago e hehe).

 

[FactChecker]

"Strong" and "weak" are subjective terms. Look at your graph for the 0.5 < r < 0.87. It certainly shows a tendency of the X values hinting at the Y values. But then look at a particular X value and notice that the Y values can vary by a large magnitude there. So there is a judgment call on whether you want to consider that "strong" or "weak". Some uses require very high standards and others accept lesser standards.